The packet type (PT)-based framework~\cite{zhang2026taming} provides a systematic and principled approach to designing device-to-device (D2D) coded caching schemes that achieve reduced \sbp while preserving the optimal communication rate. However, existing PT designs rely exclusively on homogeneous \sbp, where all packets have an identical size regardless of their types. This restriction limits the achievable \sbp reduction in certain parameter regimes. In this paper, we extend the PT framework to \emph{heterogeneous} \sbp, allowing packet sizes to vary across types under a refined type classification. The packet sizes, in conjunction with user grouping and multicast transmitter selection, are jointly optimized to minimize the overall \sbp level while preserving the optimal rate. Based on the heterogeneous PT framework, we construct a new class of D2D coded caching schemes for $(K, KM/N)=(2q+1, 2r)$ with $q,r \in \mathbb{N}_+$, where $K,N$ and $M$ denote the number of users, files and cache memory size, respectively. The proposed construction achieves a constant-factor reduction in \sbp compared to the Ji-Caire-Molisch (JCM) caching scheme~\cite{ji2016fundamental} and complements existing PT designs that are not applicable in this parameter regime.

翻译：基于数据包类型（PT）的框架~\cite{zhang2026taming}提供了一种系统化且原则性的方法来设计设备到设备（D2D）编码缓存方案，该方案能在保持最优通信速率的同时降低子包化程度。然而，现有PT设计完全依赖于同构子包化，其中所有数据包无论类型如何均具有相同大小。这种限制在某些参数范围内制约了子包化程度的可降低幅度。本文我们将PT框架扩展至异构子包化，允许在精细化类型分类下数据包大小跨类型变化。通过联合优化数据包大小、用户分组与多播发射机选择，在保持最优速率的同时最小化整体子包化水平。基于异构PT框架，我们为参数$(K, KM/N)=(2q+1, 2r)$（其中$q,r \in \mathbb{N}_+$，$K$、$N$和$M$分别表示用户数、文件数和缓存内存大小）构建了一类新的D2D编码缓存方案。与Ji-Caire-Molisch（JCM）缓存方案~\cite{ji2016fundamental}相比，所提方案实现了子包化程度的常数倍缩减，并补充了在该参数范围内无法应用的现有PT设计。